In view of the recent explosive accumulation of data on DNA sequences, it is important for the analysis of these data to have adequate mathematical models and statistical methods. During the past year work has continued on studying the properties of the coalescent process for samples of genes from populations undergoing selection. Four topics were investigated. (1) The structure of the coalescent process for a neutral locus linked to a selected locus was determined. This work was needed to determine the analytic properties of a new statistical method for identifying the presence of selection. (2) To obtain numerical results for the coalescent process for selective models often requires solving a system of nonstandard singular second order differential equations. Since standard software packages do not succeed here, it was necessary to develop a numerical recipe especially suited to this system. (3) The coalescent process was used to study the evolutionary effects of periodic selection. This work showed that the pertinent parameter is r/s where r is the rate of recombination and s is the strength of selection. (4) The final area deals with the coalescent process for subdivided populations, in particular populations that are undergoing selection. This work is relevant to the analysis of recent Adh data for D. melanogaster.